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Research Papers

Postbuckling of Hyperelastic Plates

[+] Author and Article Information
Chi Zhang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Jian Wu

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: wujian@tsinghua.edu.cn

Keh-Chih Hwang

AML,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China
e-mail: huangkz@tsinghua.edu.cn

Yonggang Huang

Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208;
Department of Mechanical Engineering, Northwestern University,
Evanston, IL 60208;
Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208;
Skin Disease Research Center,
Northwestern University,
Evanston, IL 60208

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 7, 2016; final manuscript received February 22, 2016; published online March 17, 2016. Assoc. Editor: Arun Shukla.

J. Appl. Mech 83(5), 051012 (Mar 17, 2016) (7 pages) Paper No: JAM-16-1012; doi: 10.1115/1.4032857 History: Received January 07, 2016; Revised February 22, 2016

Abstract

Curvature is simply expressed as the second derivative of the plate deflection in prior studies of post-buckling of plates. It is shown in this paper that the higher-order terms in curvature should be retained, consistent with Koiter's post-buckling theory. This paper also solves the dilemma whether the increase of post-buckling load is proportional to the square of the ratio of the post-buckling deflection w to the plate thickness t, $(w/t)2$, as in most prior studies, or to the characteristic in-plane length L of the plate, $(w/L)2$, as discovered in some recent studies.

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References

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Figures

Fig. 1

A simply supported rectangular plate subjected to pressure on four edges

Fig. 3

The boundary conditions of a rectangular plate with one clamped edge opposite to a simply supported edge: (a) illustration of the out-of-plane boundary conditions and (b) illustration of the in-plane boundary conditions

Fig. 4

The ratio of load to critical load versus the normalized out-of-plane displacement with and without higher-order terms of curvature

Fig. 2

The ratio of load to critical load versus the normalized out-of-plane displacement ((1−ν2)(1+μ4)/1+μ2)(Umax3/t) during post-buckling

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